(\partial)/(\partial x)(x^{y^x})

Lösung

\frac{\partial}{\partial x} (x^{y^{x}})

x^{y^{x}} (y^{x} ln (x) ln (y) + \frac{y ^{x}}{x})

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{y^{x}})

Behandle

y

als Konstante

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{y^{x}} = e^{y^{x} l n (x)}

= \frac{\partial}{\partial x} (e^{y^{x} l n (x)})

Wende die Kettenregel an:

e^{y^{x} l n (x)} \frac{\partial}{\partial x} (y^{x} ln (x))

= e^{y^{x} l n (x)} \frac{\partial}{\partial x} (y^{x} ln (x))

\frac{\partial}{\partial x} (y^{x} ln (x)) = y^{x} ln (y) ln (x) + \frac{y ^{x}}{x}

= e^{y^{x} l n (x)} (y^{x} ln (y) ln (x) + \frac{y ^{x}}{x})

e^{y^{x} l n (x)} = x^{y^{x}}

= x^{y^{x}} (y^{x} ln (x) ln (y) + \frac{y ^{x}}{x})

\int \frac{1}{x ^{2} + 64} d x

t an g e n t y = 2 x^{3} - x^{2} + 2

\int \frac{e ^{x^{n}}}{x ^{1 - n}} d x

h \to 0 lim (\frac{5 e ^{x} - 5 e ^{x + h}}{3 h})

in v erse l a pl a ce \frac{e ^{- s}}{( s ^{2} + 8 )}